1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Yanka [14]
3 years ago
5

Which system of linear inequalities is represented by the graph?  ax – 3y > 6 and y > 2x + 4 bx + 3y > 6 and y > 2x 

+ 4 cx + 3y > 6 and y > 2x – 4 dx – 3y > 6 and y > 2x – 4

Mathematics
2 answers:
guapka [62]3 years ago
6 0

The lines represent the inequalities \boxed{bx + 3y > 6} and \boxed{y > 2x + 4}.

Further explanation:

The linear equation with slope m and intercept c is given as follows.

\boxed{y = mx + c}

The formula for slope of line with points \left( {{x_1},{y_1}} \right) and \left( {{x_2},{y_2}}\right) can be expressed as,

\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}

Given:

The inequalities are as follows.

1.ax - 3y > 6{\text{ and }}y > 2x + 4

2. bx + 3y > 6{\text{ and }}y > 2x + 4

3.cx + 3y > 6{\text{ and }}y > 2x - 4

4. dx - 3y > 6{\text{ and }}y > 2x - 4

Explanation:

The blue line intersects y-axis at\left( {0,4} \right), therefore the y-intercept is 4.

The blue line intersect the points that are \left( {-2,0}\right) and \left( {0,4}\right).

The slope of the line can be obtained as follows.

\begin{aligned}m&=\frac{{4 - 0}}{{0 - \left({ - 2}\right)}}\\&=\frac{4}{2}\\&=2\\\end{aligned}

The slope of the line is m = 2.

Now check whether the inequality included origin or not.

Substitute \left( {0,0}\right) in equation y=2x+4.

\begin{aligned}0 &> 2\left( 0 \right) + 4 \hfill\\0 &> 4 \hfill\\\end{aligned}

0 is not greater than 4 which mean that the inequality doesn’t include origin.

Therefore, the blue line is y > 2x + 4.

Solve inequality ax-3y > 6 to obtain the standard form of inequality.

\begin{aligned}ax - 3y &> 6 \hfill\\ax - 6 &> 3y \hfill\\y &< \frac{{ax - 6}}{3}\hfill \\y &< \frac{a}{3}x - 2\hfill\\\end{aligned}

The y intercept of the equation is -2 and the y-intercept of the line is 2.

Therefore, the inequality doesn’t satisfy the line.

Solve inequality bx + 3y > 6 to obtain the standard form of inequality.

\begin{aligned}bx + 3y &> 6 \hfill \\3y &> 6 - bx \hfill\\y &< \frac{{6 - bx}}{3} \hfill\\y &< - \frac{{bx}}{3} + 2 \hfill\\\end{aligned}

The y intercept of the equation is 2 and the y-intercept of the line is 2.

Therefore, the inequality bx + 3y > 6 satisfies the line.

Option 1 is not correct as it doesn’t satisfy the inequalities of the graph.

Option 2 is correct as the inequalities satisfy the graph.

Option 3 is not correct as the y-intercept is not 4.

Option 4 is not correct as the y-intercept is not 4.

Hence, \boxed{{\text{Option 2}}} is correct

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequalities

Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.

igor_vitrenko [27]3 years ago
3 0

The <em><u>correct answer</u></em> is:

bx + 3y > 6 and y > 2x + 4

Explanation:

Looking at the second inequality, the y-intercept is 4 and the slope is 2.  This means the graph of the line crosses the y-axis at (0, 4) and the line goes up 2 and over 1.  Since it is greater than, this means the graph is shaded above it.  Comparing this to the graph, the line for the blue part crosses the y-axis at (0, 4) and goes up 2 and over 1.  The graph is also shaded above the line.

For the first inequality, bx+3y > 6, we want to isolate y.  To do this, we subtract bx from each side:

bx+3y-bx > 6-bx

3y > 6-bx

Divide both sides by 3:

3y/3 > 6/3 - bx/3

y > 2 - (b/3)x

This means the line for this will have a y-intercept of 2 and decrease 1 while going over 3.  The orange section does this.  Additionally, since it is greater than, the graph should be shaded above the line.  This one is, so this is the correct answer.

You might be interested in
What is the solution to the equation?<br> 3 (4x– 1) + x = 5x – 4 (1 – 2x) + 1
Scorpion4ik [409]

Answer:

x=1

Step-by-step explanation:

12x -3 + x =5x - 4 +8x +1

13x-3=13x - 3

+3     +3

____________-

13x=13x

÷13x   ÷13x

_________

x=1

Hope this helps :D  (idk if its right srry if not)

8 0
2 years ago
Twothirds times fifteen
Dmitry [639]
The answer is 10 :)     ........
4 0
3 years ago
Read 2 more answers
The probability of winning a certain lottery is 1/77076 for people who play 908 times find the mean number of wins
Alex73 [517]

The mean is 0.0118 approximately. So option C is correct

<h3><u>Solution:</u></h3>

Given that , The probability of winning a certain lottery is \frac{1}{77076} for people who play 908 times

We have to find the mean number of wins

\text { The probability of winning a lottery }=\frac{1}{77076}

Assume that a procedure yields a binomial distribution with a trial repeated n times.

Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.

n=908, \text { probability } \mathrm{p}=\frac{1}{77076}

\text { Then, binomial mean }=n \times p

\begin{array}{l}{\mu=908 \times \frac{1}{77076}} \\\\ {\mu=\frac{908}{77076}} \\\\ {\mu=0.01178}\end{array}

Hence, the mean is 0.0118 approximately. So option C is correct.

4 0
3 years ago
A painter leans a 15 ft ladder against a building. The base of the ladder is 6 ft from the building. To the nearest foot, how hi
stiv31 [10]
Using the Pythagoras theorem 

15^2 = x^2 + h^2   where h = height of ladder on the nuiding

h^2 = 15^2 - 6^2  =  189

 = 13.75 ft to nearest hundredth
3 0
3 years ago
Read 2 more answers
Write an expression for the description: the product of 3 and p subtracted from 6
Shalnov [3]

Answer:

6 - 3p

Step-by-step explanation:

The word "product" indicates to multiply 3 and p, and "subtracted from" tells us to use subtraction.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Can somen please help me quickly!!!!!!!!!!
    7·2 answers
  • What’s the equation in slope-intercept form?
    13·1 answer
  • On Monday, Brad biked 1 4/6 miles; Tuesday, 1 3/6 miles; Wednesday, 1 5/6 miles; and Thursday, 1 4/6 miles. On which day did he
    12·2 answers
  • If the maximum acceleration that is tolerable for passengers in a subway train is 1.74 m/s2 and subway stations are located 930
    10·1 answer
  • U'LL GET BRAINLIEST IF U ANSWER FIRST
    15·1 answer
  • Can someone give me the answer and explain plz
    6·2 answers
  • Simplify the expression below.<br> 9x + 10 - 2x + 1
    7·2 answers
  • the function f(x)= x+3 represents the length of a rectangle. the function g(x)=12x-5 represents the width of the rectangle. use
    10·1 answer
  • Find the eccentricity of the ellipse<br> 4x^2 +16y^2 +32x-32y+16=0
    12·1 answer
  • It takes 2.5 yards of material to make a dress. Harley's Clothing Design estimates that they can produce 48 dresses each week. I
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!